since we are looking for \(\sin x = 0\), we look at the graph of \(\sin\), see that the graph of \(\sin\) is becoming \(0\) when \(x = 0\) or \(x = \pi\) or \(x = 2\pi\)
since all these 3 values of x are in the range \([0, 2\pi]\) , all 3 values satisfy the equation, and interval.